PayPal reported third-quarter earnings and revenue that topped Wall Street estimates on Thursday, with a surge in payment volume for its peer-to-peer payment app Venmo.

Here's how the company did compared with what Wall Street expected:

Earnings: 58 cents vs. 54 cents per share, forecast by Refinitiv.

Revenue: $3.68 billion vs. $3.66 billion, forecast by Refinitiv.

Shares of PayPal rose as much as 7.5 percent in after-hours trading Thursday and were trading near $83. The stock is up 13 percent year to date and 8 percent year over year.

The payment company's revenue grew 14 percent in the third quarter to $3.68 billion, while earnings were up 26 percent.

Total payment volume for the peer-to-peer payment app Venmo rose 78 percent in the third quarter to roughly $17 billion. Investors had been hoping for good news on Venmo, which has struggled to prove itself as a moneymaker for its parent company.

"I'm especially pleased with the strong overall momentum surrounding Venmo," PayPal CEO Daniel Schulman said on a call with analysts Thursday. "While it is still early, our monetization efforts appear to be reaching a tipping point."

PayPal's total payment volume jumped 25 percent to $143 billion during the same time frame, short of Refinitiv analysts' expectations of $145 billion.

Mobile payment growth contributed to 40 percent of that payment volume, with 45 percent growth in mobile payment volume for the quarter. Its total payment transactions surged 27 percent to 2.5 billion total for the quarter.

The company added what it called a "record" 9.1 million accounts in the third quarter, up 15 percent from last quarter, closing the quarter with a total 254 million active accounts.

PayPal raised fourth-quarter earnings guidance to a range of between 65 and 67 cents and increased quarterly revenue guidance, both in line with analysts' expectations, according to Refinitiv. It also upped its full-year earnings guidance to a range of between $2.38 and $2.40 per share, above analysts' consensus expectations of $2.34 per share.

Before the earnings report Thursday, the company announced new features and an expansion of its existing partnership with American Express, which also reported earnings after the bell. American Express customers will now be able to send money via Venmo or PayPal directly from their Amex mobile app, pay credit card bills with existing Venmo balances, and use Amex Membership Rewards points for PayPal purchases. Earlier in October, it also announced a partnership with Walmart to incorporate PayPal money services at the retail giant's stores.

Earlier this year, the company announced a $2.2 billion deal to buy European payments start-up iZettle, which prior to the announcement had been planning on going public on the Nasdaq in Stockholm. PayPal has also made deals to buy Hyperwallet, Jetlore and Simility in 2018.

"We will continue to leverage acquisitions to strengthen our two-sided platform and maintain our position as the leading global open platform for digital payments," Schulman said on the earnings call.

PayPal saw some weakness in eBay transaction volumes, which made up 11 percent of total transaction volume, down from 13 percent a year ago.

Programming Note: For more on PayPal, watch CFO John Rainey's interview on "Mad Money" tonight at 6 p.m. ET.